[Corollary 5.18 of [1]}]
For any \(p \in [1,2]\) , there exists a randomized algorithm that, given \(O(1)\) -approximate \(\ell _p\) -distances between \(n\)  points \(x_1,\dots , x_n \in ^d\) , an integer \(k \in \) , \(z \in [1,2]\) , and \(, \delta \in (0, 1/2)\) , outputs a (random) subset \(\subset [n]\)  of \((k\log (1/\delta )/)\)  points and a set of (random) weights \(\colon \rightarrow _{\ge 0}\)  which is a strong coreset for \((k, p)\) -clustering in \(\ell _p\)  with probability at least \(1-\delta \) .Corollary 5.18 is stated with \(z \ge 2\) ; however, the proof works for any \(z \in [1,2]\)  as well.
